Yet another measure transport approach to filtering
is that of [1]}, which
uses the idea of decomposable couplings to
yield
a recursive
approximation of the full Bayesian solution to the sequential
inference
problem,
using purely variational techniques (i.e., no sampling).
Outside the coupling literature,
an early attempt to devise non-Gaussian generalizations of the
EnKF is the
Gaussian mixture filter of
[2]}.
Here, the idea is to learn the forecast density via a
regularized mixture of
Gaussians.
Finally, we note that complementary approaches to non-Gaussian high dimensional
filtering include hybrid filters [3]}
and local weights
particle filters [4]}.
These algorithms
provide an alternative route to the regularization of
SMC methods, which are
usually
consistent but plagued by large estimation variance in high dimensions.
See [5]} for a recent review.
